Hidden Variables? Navigating Gender and Sexuality in Math Class

Her-story, Equity, and Persistence in Statistics 2018 WHM conference Dr. Larry Lesser, Professor, Dept. of Mathematical Sciences ([email protected]) my related dissemination: Mathematics Teacher op-ed & letter; book chapter on persisting through statistics anxiety; JSM paper on Project ACE; her-story tribute Florence; PSA as (Frontera Womens Foundation) TITLE IX Champion; my equity webpage my related service: at UTEP: many years on Womens Studies Advisory Committee & WHM Conference committee, DoE-funded Project ACE faculty, pre-tenure mentor of female prof.; at UNC: taught cohort linking my statistics class with family studies or sociology of gender classes, and

mentored UG research on female mathematicians; at AASU: gave Math & Gender paper at its first womens studies conference family background: -- my fathers mother had a distinguished math teaching career in Ft. Worth. One of her HS students wrote my dad: Your mother taught the girls we could be savvy in math right alongside the boys. your mother opened up the ordered universe for us. my mother, a former ES teacher, has been underconfident in math. my soulmate Laurie had much success as a neuroscientist, despite differential treatment. Raise your hand if you.

view mathematics as a value-free universal language whose curriculum and classroom are unaffected by stereotypes or bias regarding gender, sexual orientation, etc. Raise your hand if you. view statistics as a value-free universal language whose curriculum and classroom are unaffected by stereotypes or bias regarding gender, sexual orientation, etc.

Raise your hand if you. can name a few famous female mathematicians. Raise your hand if you. can name a few famous female statisticians. Florence Nightingale 1820-1910

AGENDA socially constructed? statistics different from mathematics or other STEM? making gender visible in statistics making (gender) inequity visible Q&A (Gender, race, and) statistics are socially constructed We tend to envision statistics as little nuggets of truth that we uncover, much as rock collectors find stones. After all, we think, a statistic is a number, and numbers

seem solid, factual, proof that somebody must have actually counted something. But thats the point: somebody had to do the counting. Wed do better to think of statistics as jewels: jewels must be selected, cut, polished, and placed in settings so that they can be viewed from particular angles. In much the same way, people create statistics; they choose what to count, how to go about counting, and which of the resulting numbers they will share with others. Numbers do not exist independent of people; understanding numbers requires knowing who counted what, and why. This is what is meant by saying that statistics are socially constructed. -- Joel Best, 2002 JSM Proceedings

AGENDA socially constructed? statistics different from mathematics or other STEM? making gender visible in statistics making (gender) inequity visible Q&A within the mathematical sciences. (Abra Brisbin & Ursula Whitcher, 2018)

Women flocking to statistics, the newly hot, high-tech field of data science (Brigid Schulte, 12/19/14 Washington Post article) Barely 18% of computer science degrees go to women. Women make up 11% of math faculty. Nearly half of the women who graduate with engineering degrees never enter the profession, or leave soon after. More than 40% of degrees in statistics go to women, and they make up 40% of the [tenure-track] statistics department faculty. Possible factors: women tend to be drawn to more collaborative sciences that rely on teamwork and communication, establishing a critical mass of

more than 20% women, creating a welcoming environment, promoting female leaders to serve as role models AGENDA socially constructed? statistics different from mathematics or other STEM? making gender visible in statistics making (gender) inequity visible Q&A

Making gender visible in statistics. https://genderstats.un.org and http://genderstats.org/ ASA Caucus for Women in Statistics, 1971 ASA Committee on Women in Statistics, 1972 Awards such as FN David Award, Elizabeth Scott Award, Gertrude Cox scholarship award, etc. Women in Statistics and Data Science conference, 2016 Berkeley statistics professor Dr. Elizabeth Scott spent the last two decades of her life analyzing academic salary inequity (see Dec. 2017 Significance article about her); also see work of Dr. Mary Gray 2017 JSM session on implicit bias Need sex-differentiated outcomes in economic/social conditions, data on gender-based violence, etc.

Issue: some medical (e.g., drug, toxicology) research excludes women or does not report sex-disaggregated results Making gender visible in statistics. Poster by National Center for Health Statistics Also, see: Grandma Got STEM blog SACNAS Biography Project (women category) Intersectionality & Statistics

(Bowleg, 2012) 2001 NIH Policy and Guidelines on the Inclusion of Women and Minorities as Subjects in Clinical Research Statistics might help implement intersectional approaches by using interaction effects or multilevel or hierarchal modeling, but statistical assumptions of linearity, unidimensionality, uncorrelated components may not align with intersectionality tenets 2016 GAISE College Report recommendation: Give students experience

with multivariable thinking. Intersectionality: theoretical framework tenets (Bowleg, 2012) Social identities not independent and unidimensional, but multiple and intersecting Focal/starting point are people from marginalized groups Social identities at microlevel (e.g., intersections of race, gender, SES) intersect with macrolevel structural factors (e.g., poverty, racism, sexism) to yield disparate outcomes

AGENDA socially constructed? statistics different from mathematics or other STEM? making gender visible in statistics making (gender) inequity visible Q&A Statistics is needed to explore equity

(Lesser 2007 J. of Statistics Education paper) Calculating expected value of a fair share and how much deviation might be viewed as innocuous offers a benchmark to discussions about what is fair. Tools to identify group differences or patterns can help people recognize, analyze or address social inequalities Pre-K-12 GAISE Level C (high school):

students make design for differences, compare group to group using displays & measures of variability, quantification of association Areas for explorations of equity identified by Pollack & Wunderlich (table in June 2005 Amstat News is reproduced in Lesser 2007) Labor markets: hiring, interviewing, wages, evaluation, promotion, layoffs, rehiring

Education: college acceptance, financial aid, track placement, evaluation, special ed. placement, promotion Housing: steering, mortgage redlining, loan pricing, resale value; wealth accumulation Criminal justice: police behaviors, arrests, police treatment, legal representation, parole, sentencing Health care: access, insurance, quality, price, referrals (gender) equity can be a real-life context in math/stat class.

1972 Title IX law: federally-funded institutions cant discriminate on basis of sex There must be substantial proportionality between participation of women in intercollegiate athletics and their representation in the student body. In 1997, the Supreme Court ruled against Brown University:

. student body men 2796 (49%) women 2926 (51%) athletes

555 (62%) 342 (38%) of course, TITLE IX is not just about sports 2011 PSA as (Frontera Womens Foundation) TITLE IX Champion Investigating Hiring Discrimination (Kansas State U.s J.J. Higgins)

A company will hire 14 people by choosing at random from large pool with equal numbers of equally-qualified M & W. How likely is hiring 7 & 7? (only 21% chance) What deviation from this would feel suspicious in the real world..? (8 & 6? 9 & 5? 10 & 4? 11 & 3? 12 & 2? 13 & 1? 14 & 0?) Motivation for binomial distribution! Binary outcomes on each trial (bi-nom; male or female) Independence of trials

Number (e.g., 14) of trials is fixed Same probability of success (e.g., hired person is female) on each trial formula nCx px(1-p)n-x, EXCEL binomdist, or TI-84 commands where n =14, p =.5 x (number of successes) Probability of exactly x successes TI-84s 2nd DISTR Binompdf(n, p, x)

Probability of x or fewer successes TI-84s 2nd DISTR Binomcdf(n, p, x) 0 1 2 3 4 5 6

7 8 9 10 11 12 13 14 .000

.001 .006 .022 .061 .122 .183 .209 .183 .122 .061

.022 .006 .001 .000 .000 .001 .006 .029 (p <.05) .090

.212 .395 .605 .788 .910 .971 .994 .999 1.000 1.000

Power of statistics to detect invisible prejudice! (Lesser, 2010) Disguised-gender experiments (show adults treat babies differently, based on what gender they are told the baby is) Males randomly assigned to view tape of pos. or neg. feedback more likely to deem deliverer of neg. feedback as incompetent if female Stereotype experiments reviewed in my April 2014 Mathematics Teacher op ed Internet field experiment shows discrimination against same sex couples on housing market

Randomized response, list experiments, etc. Power of statistics to detect invisible prejudice! (Lesser, 2010) Example of list experiment (adapted from Kulinski et al., 1997): From your list of items, state how many upset you: *The US government increasing the gasoline tax. *Pro athletes getting million-dollar contracts. *Large corporations polluting the environment.

*[half the people get a sensitive 4th item inserted] What could we estimate if the 3-item group had a mean of 1.6 items that upset them, and the 4-item group had a mean of 2.3 items? Power of statistics to detect invisible prejudice! (Lesser, 2010) Example of list experiment (adapted from Kulinski et al., 1997): the 3-item group had a mean of 1.6 items that upset them, and the 4-item group had a mean of 2.3 items 2.3 1.6 = 0.7 = 70%,

so we estimate that 70% of the respondents are upset by the topic in the additional (sensitive) item Analyzing gender equity reporting in the media Exploring Gender-Based Differences in Earnings (Sinclair CCs K. Rowell)

State independent & dependent variables State Ho and Ha Make cross-tabulation from data to examine hypothesis

Now, control for education (< HS, HS, some college, college degree, etc.) Now, control for occupation (blue collar jobs, service jobs, white collar jobs, etc.) What other factors might account for earning differences? How much of gender gap in earnings appears to be due to gender discrimination? Strategy: connect with current events/calendar March: International Womens Day (March 8); Womens History Month April: Equal Pay Day (April 20) http://www.pay-equity.org/day.html October: I gave an intro. statistics writing assignment for students to find

and reflect on statistics related to subjects of: Breast Cancer Awareness Month; Domestic Violence Awareness Month; or LGBT History Month also, birthdays of famous women in statistics (e.g., Gertrude Cox, Jan. 13; Florence Nightingale, May 12) AGENDA socially constructed? statistics different from mathematics or other STEM?

making gender visible in statistics making (gender) inequity visible Q&A Her-story, Equity, and Persistence in Statistics 2018 WHM conference Dr. Larry Lesser, Professor, Dept. of Mathematical Sciences ([email protected]) my related published work: 2008 JSM Proceedings paper on Project ACE; 2011 PSA as (Frontera Womens Foundation) TITLE IX Champion;

2014 Rowman & Littlefield book chapter on persisting through statistics anxiety (on UTEP Library e-reserve under MATH 5364); April 2014 Mathematics Teacher op-ed & Aug. 2016 letter; 2017 her-story tribute Florence; my equity webpage, http://www.math.utep.edu/Faculty/lesser/equity.html THANK YOU FOR YOUR ATTENDANCE TODAY! WHAT ARE YOUR QUESTIONS? examples from CULTURE From F in Exams calendar page for

May 6, 2013 (thanks, Kristin G!) There are 300 students in the 10th grade. Mary and Mark want to find out the 10th grades favorite color. Mary asks 30 people. Mark asks 150 people. Mark says, My conclusions are more likely to be reliable than Marys. Why does Mark think he is right? from F in Exams calendar page for May 6, 2013 (thanks, Kristin G!)

There are 300 students in the 10th grade. Mary and Mark want to find out the 10th grades favorite color. Mary asks 30 people. Mark asks 150 people. Mark says, My conclusions are more likely to be reliable than Marys. Why does Mark think he is right? an actual student answer: Because Mark is a man Consider this. (Sharon Begley, 2008)

The Study of Mathematically Precocious Youth found a boy-to-girl ratio of 13:1 in 1983 for kids < 13 who score 700 on the math SAT, but it was 2.8 :1 in 2005. Nothing hard-wired in the brain can change that quickly. Countries whose girls excel in the Olympiad have cultures that promote math as not mainly for boys and not only for nerds.

Lesser (2014) notes randomized experiments show that ....when gender identity or stereotypes (even gender stereotypes unrelated to math ability) were evoked, women not only performed worse on mathematical items but also indicated decreased motivation to improve ....women perform worse on mathematics tests after attention is given to their appearance or attractiveness Draw a Mathematician studies Picker & Berry)

(e.g., my April 2014 Mathematics Teacher op-ed was sparked by a joke book! book had disclaimer (p. 10) that some of its jokes are appropriate for a high school classroom, while others should only be told at the pub. is such a distinction appropriate?

Math Jokes 4 Mathy Folks (Vennebush, 2012) An attractive female accountant was having a drink when the man next to her asked for her phone number. She paused for a moment, and then replied, Im sorry, Ive seen so many figures today. I just cant remember my exact telephone number but I can probably estimate it to within 10 percent. (p. 114)

Math Jokes 4 Mathy Folks (Vennebush, 2012) A statistics professor was completing what he thought was a very inspiring lecture on the importance of significance testing in todays world. A young nursing student in the front row sheepishly raised her hand and asked, But, sir, why do nurses have to take statistics? The professor thought for a few seconds

and replied, Young lady, statistics saves lives! The nursing student was utterly surprised and after a short pause retorted, But, sir, please tell us how statistics saves lives! Well, the professor said angrily, Statistics keeps idiots out of the nursing profession! (p. 96) Math Jokes 4 Mathy Folks (Vennebush, 2012)

A statistics professor was completing what he thought was a very inspiring lecture on the importance of significance testing in todays world. A young nursing student in the front row sheepishly raised her hand and asked, But, sir, why do nurses have to take statistics? The professor thought for a few seconds and replied, Young lady, statistics saves lives! The nursing student was utterly surprised and after a short pause retorted, But, sir, please tell us how statistics saves lives! Well, the professor said angrily, Statistics keeps idiots out of the nursing profession! (p. 96)

Now lets look at examples from CURRICULUM Body image example: Jessica Utts 2015 textbook Seeing through Statistics (p. 55, italics in original) Suppose a womans weight varies between 140 and 150 pounds, but when asked her weight she always answers (optimistically!)

that its 140 pounds. Then her answer is reliable, but it is not valid (except on the days when she really does weight [sic] 140). Her response is biased in the low direction. my 2016 letter to Mathematics Teacher how might this HW exercise be changed?

A student wonders if tall women tend to date taller men than do short women. (FAPP 7/e, 2006, p. 250, #47) how might this HW exercise be changed? A student wonders if tall women tend to date taller men than do short women. (FAPP 7/e, 2006, p. 250, #47) A student wonders if tall women tend to date taller people

than do short women. (FAPP 8/e, 2009, p. 208, #47) Curriculum: Perkowski & Perkowski (2007) survey results from 1990 census data from counties in south central Missouri: Curriculum: adapted from question 10 in #25 AP review sheet from a 2015-16 HS AP statistics class A research firm wants to determine whether there's a difference between what

men earn and what women earn. The firm takes a random sample of married couples and measures the annual salary of each man and woman. What procedure should the firm use to analyze the data for the mean difference in salary between men and women? a) One-sample t procedure, matched pair b) Two-sample t procedure c) One-sample z procedure, matched pair d) Two-sample z procedure e) Not enough information to determine which procedure should be used.

$885,000 Womens Educational Equity Act grant (PI: Josie Tinajero) from US Dept. of Ed., 2005-10 10 university faculty in multiple departments redesigning a wide range of courses, including: bilingual/ESL ed, mathematics, statistics, physical science, critical pedagogy, & multicultural ed ACE offered workshops, webinars, seminars, articles, and other professional development on relevant issues, including: service learning, gender issues in the classroom, & gender/equity issues in STEM fields Project ACE Goals include:

increase access to higher ed for girls, women, and underrepresented minorities (Females are among the groups who have traditionally been far more likelyto be the victims of low expectations, NCTM 2000, p. 13). raise awareness about opportunities in STEM careers for young women engage future/current teachers in planning, implementation and evaluation of community service learning activities that will enhance educational equity and solve community problems

I taught my Project ACE version of intro. stat. in fall 2007, 2008, 2009 to 52, 29, and 68 students, respectively at a mid-sized research university on US-Mxico border stat literacy approach: Utts Seeing Through Statistics: ch.1-11,16+) (I coordinate) all 5 sections/semester preservice teachers (most ES, some MS) mostly female (2007: 79% of mine were)

mostly Latina/o many first-generation students starting fall 2009, a few Core Curriculum students join the teachers anonymous post-survey (N=43) of my 2007 students: prior interest in subject: high (9.3%)

average (27.9%) low (53.5%) unsure ( 9.3%) reason for taking class: requirement (100%), elective (0%) goals for my fall 2007 ACE Stat 1380 included: Provide students tools to describe and assess equity. Have students explore specific examples or activities that involve gender equity. Offer project opportunity that connects to gender equity, social justice

or service learning. Use pedagogy that gives both genders full chance to participate and learn! Classroom Strategies Humanize subject matter by showing how it came from, connects to, and can be used to help the real-world. Mention specific male & female contributors to the field. (resource: www.sacnas.org/biography/) Give males & females equal opportunities to answer questions of comparable complexity. Provide opportunities for (non-competitive) collaborative learning, and when forming groups, make sure no group has only 1 female, and have roles rotate or randomly assigned

And.. ??? Some Methods Used Discussion of equity examples (El Paso Portraits: Womens Lives, Potential and Opportunities) Launching webpage of resources: www.math.utep.edu/Faculty/lesser/equity.html More collaborative learning (including most quizzes and projects) Discussed my STEM work as statistician outside academia; modeled my work as a statistics education researcher

Connections to state (e.g., TEKS, TAKS) and national standards (e.g., K-12 GAISE, NCTM Standards, & Curriculum Focal Points) More modeling of technology (TI-73, Excel, applets) & manipulatives, including hands-on computer work Final project (authentic assessment) Some written reflections I assigned FALL 2008: Read through the report posted at http://womensfundofelpaso.org/NeedsReport.pdf Discuss how, if at all, the knowledge of probability and statistics you have gained this year affected what you are able to notice and understand in this report. Explain the importance

of statistics in helping understand and improve the situation of women in El Paso. FALL 2009: Questions about S. Begleys column (9/14/09 Newsweek) include: Are disguised gender experiments necessary to learn whether people treat babies differently based on the babies gender? Explain. Does the research discussed in the article support or not support the idea that girls and boys have equal potentials to pursue a career in the STEM fields? Explain. some accompanying Project ACE narrative explanations (2007 post-survey; 2008 post-survey)

We can use statistics to see if a company is baised against women. We can use math #s to determine the rate of hiring women. Doing research, interviews, questionaires and statistic projects, we were able to really explore gender equity and gender bias as we implemented the skilled we learned in this class. I would show my students a graph comparing the wages of females and males on a specific profession instead of just simply talking about it. this class has taught me how to look at things in a different way thru different angles & not just look at whats in front of you Julia

for Julia Louise (Shanblum) Lesser, 1907-1981 Power of statistics to detect invisible prejudice! (Lesser, 2010) Randomized Response (Warner, 1965) Simple version: State yes/no question where YES is sensitive. Each person privately flips coin. If HEADS, say YES. If TAILS, answer truthfully.

Example: Suppose when 50 students are asked with RR Are girls innately worse at math than boys?, we get 32 YESes and 18 NOs. Estimate proportion who believe girls are worse. Power of statistics to detect invisible prejudice! (Lesser, 2010) Randomized Response (Warner, 1965) If HEADS, say YES. If TAILS, answer truthfully.

Example: Suppose when 50 students are asked with RR Are girls innately worse at math than boys?, we get 32 YESes and 18 NOs. We estimate 36 NOs, which 50-36 = 14 YESes, so 14/50 = .28 of sample is estimated as true YES. (Note: other RR versions can handle questions where YES and NO are both sensitive.) a pitfall of salary comparisons

(from Lesser, 2001): Find mean salary for men Find mean salary for women Complete the sentence: A woman earns ___ to a mans dollar. a pitfall of salary comparisons (from Lesser (2001)):

Mean salary for men: 41,000 = (70*20,000+30*90,000)/100 Mean salary for women: 37,000 = (90*30,000+10*100,000)/100; (this is 90 to a mans dollar) Importance of Simpsons paradox awareness that a comparison can be affected by how data is aggregated is listed by the National Council on Education and the Disciplines (2001) as essential for democracy

, Another application: jury discrimination (G. Michailides, UCLA) In 1969, Dr. Benjamin Spock came to trial in Bostons Federal courthouse. A panel of 350 selected by Judge Fords clerk had 29.1% W

(though 53% of eligible jurors were W). From these 350, the 100 potential jurors Judge Ford chose included 9 W. Discuss! Another application: jury discrimination UCLA) (G. Michailides, Stage 1: from population thats 53% W, panel of 350 chosen with 102 (29.1%) W

Stage 2: from panel of 350, the 100 that are chosen include 9 W ----------------------------------------------------- Stage 1: Binomcdf(350, .53, 102) = Prob( 102 women) = 1.4 x 10-19 or about 1 in 7 quintillion or use normal approximation: z = (.291-.53)/sqrt[.53(1-.53)/350] = -8.9 Stage 2: Binomcdf(100, .291, 9) = Prob( 9 women) = 9.5 x 10-7 or about 1 in 1 million

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